which follows from the rules of calculus. The coefficients of the variations of \(\delta \rho (x)\)  and \(\delta \Phi (x)\)  are then identified as the functional derivatives with respect to \(\rho (x)\)  and \(\Phi (x)\) , respectively; one can think of these as the generalization of a partial derivative to spaces of infinite dimensions (see e.g., ch.2 of [1]} for an introduction).
